Transport coefficients for higher dimensional quantum Hall effect

TL;DR

This paper extends the understanding of quantum Hall effect in higher dimensions by deriving bulk effective actions, incorporating band structures, and providing explicit formulas for Hall viscosity in multiple dimensions.

Contribution

It introduces a method to include electronic band structures into the effective action and derives explicit formulas for Hall viscosity in higher-dimensional quantum Hall systems.

Findings

Derived bulk effective actions using Chern-Simons terms.

Expressed Hall currents and conductivities via Chern classes.

Provided explicit formulas for Hall viscosity in 2+1 and 4+1 dimensions.

Abstract

An effective action for the bulk dynamics of quantum Hall effect in arbitrary even spatial dimensions was obtained some time ago in terms of a Chern-Simons term associated with the Dolbeault index theorem. Here we explore further properties of this action, showing how electronic band structures can be incorporated, obtaining Hall currents and conductivity (for arbitrary dimensions) in terms of integrals of Chern classes for the bands. We also derive the expression for Hall viscosity from the effective action. Explicit formulae for the Hall viscosity are given for 2+1 and 4+1dimensions.